Be able to perform simple programming tasks using any platform (preferably Octave)

Homework, Projects, and all other assignments will be submitted in electronic format

No homework assignments need to be submitted, they are just for personal practice and solutions will be provided.

Course Objectives

This course is designed to introduce the learner to the principles of structural vibration. It introduced the concepts of multiple degree of freedom systems and simple structures and their applications. The learner will be able to analyze and design the dynamics of simple structures under harmonic and general excitations in the frequency and time domains.

Assessment Tools

T1: Examinations/Tests
T3: Group Projects
T6: Student Survey

Course Intended Learning Outcomes

By the end of this course, the student will be able to:

ILO#

Description

Assessment
Tool

Program
ILO

1

Evaluate the natural frequencies and mode shapes of multiple degree of freedom systems

T1,T6

1

2

Evaluate the frequency response of multiple degree of freedom systems

T1,T6

1

3

Design vibration absorbers

T1,T6

1

4

Understand the basics of vibration attenuation and instability

T1,T6

1

5

Determine the natural frequencies and mode shapes of simple continuous structures

T1,T6

1

6

Apply the concepts of periodic structures on bars and beams

T1,T6

10

7

Create an experiment to analyze the vibration of structures

T1,T6

2,4,5,11

8

Understand the basic concepts of aeroelasticity.

T1,T6

10

10

Work in a multifunctional team

T3,T6

4

11

Prepare and present technical work results

T3,T6

2,7,11

References

Lecture Notes

Online resources

Engineering Vibration, 4th Edition, Daniel J. Inman,

Topics and Schedule

Week #

Topic

Practice and Assessment

ILO's

1 5/2/2017

Introduction
- Course outline and Objectives
- Course Assessment
- Why we study Vibration
- The concept of resonance
- The concept of vibration control
- The concept of vibration based health monitoring

Discrete Systems
- What is a degree of freedom
- Single degree of freedom systems
- Mass-Spring Systems
- Equation of motion
- Solving the equation of motion
- The natural frequency and resonance
- Presenting the solution in different forms
- Response to harmonic excitations – Time and frequency domains
- Examples
- Pendulum
- Inverted pendulum and instability
- Base excitation
- ...

1,4

2 12/2/2017

Damping
- What is damping
- Different types of damping
- The dash-pot damper
- Equation of motion for mass-spring-damper system
- Solving the equation of motion
- The damped natural frequency
- Different presentations of the solution
- Effect of damping on resonance – Time response
- Effect of damping on resonance – Frequency response
- Critical damping
- Examples
- ...

2-Degree of freedom (2-DOF) systems
- Examples of 2-DOF
- Equations of motion for discrete mass-spring system
- Solving the equations of motion
- Natural frequencies
- Mode shapes
- Time domain response
- Frequency response
- The vibration absorber
- Introducing damping
- Examples
- Car and wheel Vibration Absorber

Hamilton method of deriving equations of motion
- Potential energy
- Kinetic Energy
- External work
- Hamilton method
- Deriving the equations for 2-DOF system
- Deriving the equations for pendulum and cart problem

Continuous Structures
- Vibration of cables and strings
- Equations of motions
- Solving the equations of motions
- Natural frequencies
- Mode shapes

Midterm #1

5

7 19/3/2017

Vibration of bars
- Equations of motions
- Boundary conditions
- Solving the equations of motion
- Natural frequencies and mode shapes
- Special boundary conditions
- Periodic bars
- Damping of bar vibration using viscoeleastic materials
- Vibration control using piezoelectric material

Second Presentation of project

5,6

8 26/3/2017

Vibration of Shafts
- Equations of motions
- Boundary conditions
- Solving the equations of motion
- Natural frequencies and mode shapes
- Special boundary conditions

5

9 2/4/2017

Vibration of Beams
- Equations of motions
- Boundary conditions
- Solving the equations of motion
- Natural frequencies and mode shapes
- Special boundary conditions

5

10 9/4/2017

Vibration of beams
- Effect of axial loading on natural frequencies
- Periodic beams

20% Final (You must obtain at least 50% of the final score to pass the course)
15% Midterms 7th, 12th week(All counted)
5% Random pop-quizzes (3-8 quizzes) (All counted)
60% Course Project

Course Project

Topics

All experiments will utilize a shaker and a function generator

The topics should include the design and creation of a vibration experiment

All experiments should include the preparation and operation of a microcontroller-based data collection device that interface with a computer (Penalty up to 10% for using ready-made data collection devices)

All experiments should include the creation of software for analysis of the collected data based on open source packages or compilers (penalty up to 10% for use of ready-made analysis software, and another 10% for using non open source software or platform)

The mechanical design should be performed on open source packages except in the functions that are not available on any open source package. (penalty up to 10% for using non open source packages)

Teams

The team should include four to eight students who will devide themselves into subteams working on hardware ans software developments.

Project Evaluation

Project management (15%) (3 5-minute presentations by team coordinators)

Planning (40%)

Follow up (20%)

Corrective actions and replanning (40%)

Final Report (15%)

Technical report format (Cover, TOC, Introduction and literature survey, mathematical background, experimental design, results, conclusions, reference, appendices) (25%)

Rigour of literature survey (25%)

Details of the experimental design (25%)

Data collected from the experiment and its analysis (25%)

Experimental Hardware (20%)

Packaging (25%)

Ease of use and operability (25%)

Percision of measuements (25%)

Cost optimization (25%)

Data collection hardware (20%)

Packaging (25%)

Stability and reuseability (25%)

Ease of use and operability (25%)

Cost optimization (25%)

Software (20%)

Ease of use and operability (30%)

Accuracy (40%)

Output graphics (40%)

Final presentation (10%)

Public decimation of knowledge (Website. Wiki, videos, public slides, public reports, design graphics and charts, etc...) (25%)

Presentation graphics and appeal (15%)

Accuracy of presentation content (15%)

Comprehensability of presentation content (15%)

Audience capturing (10%)

Audience participation and reply to questions (10%)

## Important Requirements

All students are required to## Course Objectives

This course is designed to introduce the learner to the principles of structural vibration. It introduced the concepts of multiple degree of freedom systems and simple structures and their applications. The learner will be able to analyze and design the dynamics of simple structures under harmonic and general excitations in the frequency and time domains.## Assessment Tools

T1: Examinations/TestsT3: Group Projects

T6: Student Survey

## Course Intended Learning Outcomes

By the end of this course, the student will be able to:Tool

ILO

## References

## Topics and Schedule

5/2/2017

- Course outline and Objectives

- Course Assessment

- Why we study Vibration

- The concept of resonance

- The concept of vibration control

- The concept of vibration based health monitoring

Discrete Systems

- What is a degree of freedom

- Single degree of freedom systems

- Mass-Spring Systems

- Equation of motion

- Solving the equation of motion

- The natural frequency and resonance

- Presenting the solution in different forms

- Response to harmonic excitations – Time and frequency domains

- Examples

- Pendulum

- Inverted pendulum and instability

- Base excitation

- ...

12/2/2017

- What is damping

- Different types of damping

- The dash-pot damper

- Equation of motion for mass-spring-damper system

- Solving the equation of motion

- The damped natural frequency

- Different presentations of the solution

- Effect of damping on resonance – Time response

- Effect of damping on resonance – Frequency response

- Critical damping

- Examples

- ...

19/2/2017

- ...

26/2/2017

- Examples of 2-DOF

- Equations of motion for discrete mass-spring system

- Solving the equations of motion

- Natural frequencies

- Mode shapes

- Time domain response

- Frequency response

- The vibration absorber

- Introducing damping

- Examples

- Car and wheel

Vibration Absorber

Hamilton method of deriving equations of motion

- Potential energy

- Kinetic Energy

- External work

- Hamilton method

- Deriving the equations for 2-DOF system

- Deriving the equations for pendulum and cart problem

5/3/2017

- Viscoelastic Damping

- Piezoelectric Materials

- MR Fluids

- Periodic Structures

- Active vibration Control

- Critical speeds for shafts

12/3/2017

- Vibration of cables and strings

- Equations of motions

- Solving the equations of motions

- Natural frequencies

- Mode shapes

Midterm #119/3/2017

- Equations of motions

- Boundary conditions

- Solving the equations of motion

- Natural frequencies and mode shapes

- Special boundary conditions

- Periodic bars

- Damping of bar vibration using viscoeleastic materials

- Vibration control using piezoelectric material

26/3/2017

- Equations of motions

- Boundary conditions

- Solving the equations of motion

- Natural frequencies and mode shapes

- Special boundary conditions

2/4/2017

- Equations of motions

- Boundary conditions

- Solving the equations of motion

- Natural frequencies and mode shapes

- Special boundary conditions

9/4/2017

- Effect of axial loading on natural frequencies

- Periodic beams

16/4/2017

23/4/2017

Midterm #230/4/2017

7/5/2017

Course Project due

14/5/2017

- Control Reversal

## Assessment

20% Final (You must obtain at least 50% of the final score)to pass the course15% Midterms 7th, 12th week(All counted)

5% Random pop-quizzes (3-8 quizzes) (All counted)

60% Course Project

## Course Project

## Topics

All experiments will utilize a shaker and a function generator## Teams

The team should include four to eight students who will devide themselves into subteams working on hardware ans software developments.## Project Evaluation

## Registration Form